Spectrometer based (Sp) and Swept source (SS) based interferometry and Sp-OCT and SS-OCT are technologies based on analysing the spectrum of the interference signal produced between optical signal from an object under investigation and a local optical reference signal. OCT can produce in real time a cross section image of the object, i.e. a two dimensional (2D) image in the space (lateral coordinate, axial coordinate). The two configurations for Sp-OCT and SS-OCT are described in the article “Optical coherence tomography”, by A. Podoleanu, published in Journal of Microscopy, 2012 doi: 10.1111/j.1365-2818.2012.03619.x.
With reference to FIG. 1, in prior art, a Sp or SS interferometer (OCT) system consists mainly in an interferometer, 1, and a decoder, 10, to obtain depth resolved information from an object 13 and deliver a signal 20 as an A-scan. The prior art executes spectral analysis using a Fourier transform (FT) of the electrical signal 100 proportional to the output signal from 10 (not shown in FIG. 1). The spectrum at the interferometer output presents peaks and troughs, and therefore is often referred to as channelled spectrum. The larger the optical path difference in the interferometer, the denser the modulation of the channelled spectrum.
The FT can be written as an integral transformation with a Kernel function K as follows:
                              C          ⁡                      (            l            )                          =                              ∫                          -              ∞                                      +              ∞                                ⁢                                    K              ⁡                              (                                  l                  ,                  v                                )                                      ⁢                          CS              ⁡                              (                v                )                                      ⁢                                                  ⁢            d            ⁢                                                  ⁢            v                                              (        1        )            and delivers the complex reflectivity C (reflectance and phase) of an object, 13, in depth l. The kernel of FT is defined by K(l,v)=Exp[i4πlv/c], where c is the speed of light. The integral in (1) is performed over a coordinate proportional to the optical frequency, v. Unfortunately, in practice, what is delivered by 10 is not proportional to the optical frequency. In prior art, a FT can only provide reliable results if data is resampled and reorganised in equal frequency slots. For the FT operation to work properly, prior resampling is necessary to provide the channelled spectrum in equal slots of optical frequency. Different hardware and software methods have been reported to alleviate the problem of spectral data not organised linearly.
To eliminate the need of data resampling, Master Slave interferometry and OCT method was suggested that avoids the need for a FT. Such methods and apparatuses have been disclosed in the patent application: Method and Apparatus for Processing the Signal in Spectral Domain Interferometry and Method and Apparatus for Spectral Optical Domain Coherence Tomography, WO/2014/068323, PCT/GB2013/052854, by Adrian Podoleanu and Adrian Bradu. This patent application discloses a method, termed as Master/Slave (MS), that eliminates the need of a FT. In addition, the Master/Slave method allows production of multiple en-face (C-scan) OCT images simultaneously. As seen in FIG. 1, a Master Slave apparatus uses a comparison block 2 that compares the shape of the electrical signal at the decoder 10 output with experimental Masks corresponding to a reference stored version 30p of the electrical signal output by 10, of a channelled spectrum obtained when a model object was used (instead of the object 13 ). Therefore, a single depth value, A(p), from depths p=1, 2 . . . P of the A-scan is output, 20(p). This operation distinguishes the MS method from the FT conventional method that provides all depth points, A(1), A(2), . . . A(P) of the A-scan in one FT step, i.e. all depths in a single signal. The MS-OCT method opened the avenue of a different type of processing, in parallel, where information from all depths in the object is output in parallel, along different signals (outputs), as shown in more detail in FIG. 2. This peculiar feature of the MS method allows direct parallel production of en-face OCT images from several depths in the object. In FIG. 2, to provide several points in depth from the object 13, along the A-scan, the comparison operation in 2 is repeated in parallel for as many points P of versions of experimental Masks 30(p) stored in a storage block, 3. The interferometer 1 is made up of a beam-splitter, 12, a reference mirror 14, an interface optics 15 that conveys light towards an object subject to tests or imaging 13. In case the application is optical coherence tomography, then the interface optics 15 contains a one or two lateral or transversal galvo-scanner, 151, 152, according to technology known in the art.
The decoder block of the channelled spectrum, 10, translates the channelled spectrum shape at the interferometer output into an electrical signal, 100, and uses two blocks, an optical source 11 and a reader 17. For a spectrometer based configuration, the source 11 is a broadband source 111 and the reader 17 is a spectrometer, 171. For a swept source configuration, the optical source 11 is a narrow tuneable laser 112 and the reader 17 is a fast photodetector, 172. The prior art reports on configurations driven by a broadband source with a spectrometer as reader, are denominated as spectral domain OCT, while configurations using a swept source and a photodetector are denominated as Fourier domain OCT. There are also reports using the terminology the other way around. In what follows we will refer to both types of configurations as spectral domain (SD) OCT for brevity. In prior art before the invention of the MS method, both configurations would deliver the signal output to a Fourier transform block.
The electrical (slave) signal Iu,v, 100, of the decoder 10 can be represented as a 1D array, Iu,v={Iu,v(1), . . . , Iu,v(r), . . . , Iu,v(R)}, for r=1 to R, where each component Iu,v(r), 100(r), corresponds to a resolved pixel in the spectral domain. The (u,v) represent the lateral pixels of the object 13. The minimum number of resolvable pixels is determined by the number of pixels in the linear camera used in the spectrometer 171 or as the number of temporal windows within the sweeping time of the swept source 112, in which case R is usually determined by a digitiser. The prior art based on FT suffers from nonlinear representation of the optical spectrum along the r axis.
We distinguish two types of OCT applications, retina imaging, where the tissue investigated is 13b, behind the eye lens 13a, of the object 13, when rays pivot through 13a to fan over 13b. For skin, eye anterior chamber, industrial applications, and objects of arts, the object is the sample itself, i.e. 13b. When imaging skin, objects of art, etc, as obvious for people skilled in the art, a lens 13a needs to be added to the interferometer to form an image on 13b. For simplicity from now on, the group of lens 13a and object investigated 13b are shown together as 13 and referred to, generically, as the object. Irrespective of cases, eye or skin, the optical path difference is measured up to 13b and the object imaged is practically 13b. 
The prior art MS procedure operates in two stages:
Master Stage:
An object model is used and channelled spectra termed as experimental Masks are acquired and deposited in a storage of Masks. The model object is a lens (to simulate the eye lens 13a) plus a mirror (to simulate the retina 13b) for retina imaging, while for skin, eye anterior chamber and industrial applications, the model object is a mirror only (FIG. 1). The Masks are acquired for a set P, of optical path difference (OPD) values in the OCT interferometer.
Slave Stage:
The object to be investigated replaces the model object and channelled spectra acquired are compared with the set of experimental Masks in the storage. Instead of a FT, the prior art MS method uses a comparison block 2. This uses P comparators 21(p), p=1, 2, . . . P to produce signal 20(p), made from many outputs Au,v(p), each representing a reflectance value from a depth p in the object 13, for each pixel (u,v) in the two lateral directions across the object, with u=1, 2, . .. U and v=1, 2, . . . V. The outputs Au,v(p) are obtained by comparing the electrical signal proportional to the shape of Channelled Spectra 100 with the signal provided by a Storage of Masks 3, delivering signal 30(p) to each comparator 21(p), by reading each Mask 30(p). The parallel provision of depth information along separate signals, allows simultaneous generation of en-face OCT images, as shown in FIG. 3. A-scans can also be produced, as shown in FIG. 4 for any pixel such as (u0,v0) in the two lateral directions across the object, by putting together the collection of outputs Au0,v0(1), Au0,v0(2), . . . , Au0,v0(P) signals. For each experimental mask, a comparison operation delivers a point from the OPD value used to acquire the respective mask, so P points in depth from the object are delivered that can be used to build an A-scan (as shown in FIG. 4).
In fact, in the spirit of the MS method, the Kernel K(l,v) in Eq. (1) can be seen as a Mask that interrogates the electrical signal CS 100 for a depth l. However, in the prior art of MS technology, disadvantageously, the phase of the final signal was discarded as only shapes of channelled spectra were compared.
In what follows, OPD and depth will be used interchangeably. When measured in air, the OPD is considered equal to double the value of depth. When referring to a mirror, such as to the model object, reference will be made to OPD, as it does not make sense to refer to depth here. However, different points in depth in the object, each correspond to equivalent values of OPD, made from the OPD parts measured in air plus the double of the depth value multiplied by the object index of refraction.
The prior art MS method has been employed, according to the teaching of the PCT patent application mentioned above, in generating multiple en-face OCT images (C-scans) from retina and skin as, further explained in “Master-slave interferometry for parallel spectral domain interferometry sensing and versatile 3D optical coherence tomography,” by A. Gh. Podoleanu and A. Bradu, published in Opt. Express 21, 19324-19338 (2013) and in the paper “Imaging the eye fundus with real-time en-face spectral domain optical coherence tomography, by A. Bradu and A. Gh. Podoleanu, published in “Biomed. Opt. Express. 5, 1233-1249 (2014).
The MS method has been also employed to generate cross section OCT images (B-scans), as reported in “Calibration-free B-scan images produced by master/slave optical coherence tomography,” by A. Bradu and A. Gh. Podoleanu, published in Opt. Lett. 39, 450-453 (2014).
The parallel feature of the MS method has been exemplified on the use of graphic cards in the paper “On the possibility of producing true real-time retinal cross-sectional images using a graphics processing unit enhanced master-slave optical coherence tomography system,” by Adrian Bradu, Konstantin Kapinchev, Frederick Barnes, and Adrian Podoleanu, published in J. Biomed. Opt., 20(7), 076008 (2015).
Its parallel feature was exemplified in generating both C-scans and B-scans in imaging the eye in the paper, “Master slave en-face OCT/SLO,” by Adrian Bradu, Konstantin Kapinchev, Frederick Barnes, and Adrian Podoleanu, published in Biomed. Opt. Express 6, 3655-3669 (2015).
However, the method and apparatuses protecting the prior art MS technology, disclosed in the PCT patent, FIGS. 1 and 2 and papers listed above, present several disadvantages such as:    1. The MS operation is based on a comparison of channelled spectra shapes. Phase has been discarded, while phase is important in flow and polarisation analysis to name only a few of applications.    2. To avoid the problem of phase variation (random phase) from the moment the experimental Masks were acquired at the Master stage until used at the Slave stage, the comparison operation is repeated for several lag values of wavenumber. This equates to an integral over wavenumber lag space that leads to deterioration of axial resolution achieved.    3. The number of en-face images and of points in the A-scans is limited to the number of experimentally collected Master Channelled Spectra at the Master stage, i.e. limited to P. In case the bandwidth of the broadband source in Sp-OCT is over hundreds of nm, or the tuning bandwidth of the swept source in SS-OCT is over hundreds of nm, as required by high axial resolution OCT, a huge number of experimental channelled spectra need to be acquired. This may lead to a long time consuming Master stage.    4. The limitation of number of depths in the final A-scan or of depths of C-scan images leads to under-sampling, unless a sufficient corresponding number of Master Channelled Spectra are acquired at the Master stage.    5. Also, there are configurations, such as for endoscopy, or configurations with all reference path in fibre that may not allow collection of any experimental channelled spectra to be used as masks or such a collection requires addition of devices such as translations stages, otherwise not needed.    6. To improve the resolution and the decay of the sensitivity with depth, the model presented in the paper by A. Bradu, M. Maria, A. Gh. Podoleanu, “Demonstration of tolerance to dispersion of master/slave interferometry”, published in Opt. Express 23, 14148-14161 (2015) suggests elimination of envelope of the channelled spectrum modulation by division of Master Channelled Spectra acquired at the Master stage by the power spectrum of the optical source used (the usual Gaussian shape). Then, all such experimental Masks obtained, present the same constant amplitude, in an attempt to enhance sensitivity and axial resolution. However, division operation is known to introduce noise and even more, to avoid the problem of division by small numbers, the spectrum is narrowed, leading to a worse axial resolution.    7. In order to compensate for the dispersion in the object, the prior MS art proposes to use slabs of similar material as the object at the Master stage. For instance, if the object is the retina, then a 2 cm water cuvette may be used in the model object. However, if dispersion of the retina is to be compensated for, slabs of material similar to the retina are needed, cut at thicknesses required by the steps at the Master stage. This is rather difficult, to provide hundreds of such slabs, of the same material as that investigated.
Therefore, there is a need to develop apparatuses and methods to restore, or process the phase, to eliminate the effect of random phase, simplify the Master stage operation, to allow production of C-scans and points of A-scans from any point in depth, irrespective of the depths used at the Master stage, and compensate for dispersion in the object without any slab in the model object.
There is also a need for elimination of amplitude dependence of the experimental masks on the wavenumber, dependence that in previous reports of MS implementations, translates in limitation of the achievable axial resolution and decrease of sensitivity with depth.
There is also a need to perform the MS method on OCT systems where there is difficult or impossible to acquire channelled spectra to be used as masks.